1. Spatial density approach for space debris
launch modelling
Richard Ottaway (24862436) – supervised by Dr Camilla
Colombo & Francesca Letizia (co-supervisor) Poster Board Number: 77
Time: 09:30 - 12:30
Anticipated final stages of research
This project will demonstrate whether the source/sink approach can be included in the
density based method and will function with the pre-existing spatial density models. A
traffic model will be implemented to study the evolution of space debris in LEO and
hopefully be a valuable contribution to this field of study.
References
[1] Letizia, F., et al. Multidimensional extension of the continuity equation method for debris clouds evolution. Adv. Space Res.
(2015), http://dx.doi.org/10.1016/j.asr.2015.11.035
[2] McInnes, C.R. Simple Analytic Model of the Long-Term Evolution of Nanosatellite Constellations, Journal of Guidance,
Control, and Dynamics, Vol. 23, No. 2 (2000), pp. 332-338. http://dx.doi.org/10.2514/2.4527
[3] Colombo C., Letizia F., Lewis H. G., “Spatial density approach for modelling the space debris population”, The 26th AAS/AIAA
Space Flight Mechanics Meeting, Napa, CA, 14-18 Feb. 2016, AAS 16-465.
[4] ] Gor’kavyi, N., “A new approach to dynamical evolution of interplanetary dust,” The Astrophysical
Journal, Vol. 474, No. 1, 1997, pp. 496–502,
[5] LaFleur, J.M., Extension of a Simple Model for Orbital Debris Proliferation and Mitigation, AAS 11-173, Spaceflight Mechanics
2011, Proceedings of the 21st AAS/AIAA Flight Mechanics Meeting, Feb 13-17, 2011
[6] Space-Track.org (2016) [Accessed 08/07/2016] https://www.space-track.org
Introduction
Space debris poses a huge risk to the operation of spacecraft in Earth orbit. With nearly 20,000 objects larger
than 10cm currently in orbit, it is essential to be able to predict the collision risk any new satellite will
experience during its lifetime. Traditional methods of predicting the path of space debris model each particle
individually, which is computationally expensive. By modelling the space debris environment as a cloud of
varying density, the evolution and movement of space debris can be modelled and used to predict collision
risks in different zones of the orbit.
This project focuses on designing a launch traffic model to model past and future launch data, which will be
inputted into a density cloud model [1]. The model will provide a source term ሶ𝑛+
𝑎, 𝑒 as a function of
𝑎 (Semi Major Axis) and 𝑒 (Eccentricity) to simulate the fast/discontinuous deposition of objects and
injection into orbit due to rocket launches [2]. In order to generate the launch traffic model historical launch
data is analysed and from the past history an extrapolation will be performed.
Progress so far
• Successfully matched approximately 10% of objects in the IADC and Space-Track populations for years
2005-2012.
• Investigated and compared initial distribution of each population
• Read and understood previous works in the field to apply and combine techniques
Sources and Sinks Modelling
In previous work it was proven that the continuity equation (1) can be used to study the time evolution of
the density of fragments in Earth orbit [1] and the debris population in Low Earth Orbit [3]. However, the
source and sink term ሶ𝑛+ − ሶ𝑛− has always been treated as equal to zero for these works. This project uses
historic data from debris populations to compute the ሶ𝑛+
term and input it into the model. The ሶ𝑛+
term
was defined by McInnes [2] and Gorkavyi [4] as equation (2). In this equation the ሶ𝑛 𝑚 term is the mean
number density with the deposition of new satellites centred at orbit radius 𝑟𝑑, and 𝛾 a constant to be
determined.
Aims & Objectives
• Analyse current space debris population
• Create a source function for space debris describing launches
• Implement this source term in debris cloud simulation code
• Analyse results of debris propagation
Initial Debris Distribution
The shaded histograms above illustrate the number of objects and their distribution in Low Earth Orbit,
depending on semi major axis, eccentricity and inclination.
Debris Populations and Initial Debris Distribution
With the aims of creating a traffic model, the current debris population was first analysed with focus on the new
objects launched. Three datasets were considered in this project: Two Line Element (TLE) data from Space-
Track.org [6], data from the IADC (Inter-Agency Space Debris Coordination Committee) and a database from the
UCS (Union of Concerned Scientists). Each database provides different information, as illustrated in Table 1.
It was decided that the UCS database was not complete enough to use. Instead the Space-Track and IADC
populations are being matched and combined to create a database of orbital parameters, mass, size and
classification of each object.
Previous Traffic Models
Many launch traffic models exist. The main model used in debris simulation is based on an 8-year
repeating cycle. A work completed by J. Lafleur [5] describes an alternative launch traffic model, based on
a system of two sinusoidal equations (3)(4). This model is cyclic and mathematically quite simplistic, but it
does not take into account object size or mass, so cannot be used on its own.